Dumplings -To-Go (DTG) provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants. The target for a customer's waiting time is 3.0 minutes +/- 1 minute. Each month, one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period. The data for one restaurant appears below. Calculate the process capability ratio. Is this restaurant capable of meeting DTG standards? Insert table here

A) yes
B) no
C) Cannot be determined from the above information

Question

Dumplings -To-Go (DTG) provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants. The target for a customer's waiting time is 3.0 minutes +/- 1 minute. Each month, one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period. The data for one restaurant appears below. Calculate the process capability ratio. Is this restaurant capable of meeting DTG standards? Insert table here

A) yes 
B) no 
C) Cannot be determined from the above information

Quizplus · Accepted Answer

To calculate the process capability ratio, we first need to calculate the process mean and standard deviation using the given data. Using the formula for sample mean, we get:

x-bar = (3.68 + 2.51 + 2.96 + 2.94 + 2.87 + 3.43) / 24 = 0.292

Using the formula for sample standard deviation, we get:

s = sqrt([(3.68-0.292)^2 + (2.51-0.292)^2 + ... + (3.43-0.292)^2] / 23) = 0.647

Now, the process capability ratio (Cpk) is given by:

Cpk = min[(USL - x-bar) / 3s, (x-bar - LSL) / 3s]

where USL is the upper specification limit (3+1=4) and LSL is the lower specification limit (3-1=2).

Substituting the values, we get:

Cpk = min[(4 - 0.292) / (3 x 0.647), (0.292 - 2) / (3 x 0.647)] = -0.74

Since the Cpk value is negative, it indicates that the process is not capable of meeting the DTG standards. Therefore, the best choice is B) no.

Dumplings -To-Go (DTG) Provides Take-Out Dumplings and Noodle Dishes to Customers